An Application to HB Rao yu Model Under Beta Distribution On sampel dataset

Load package and data

 library(saeHB.panel.beta)
 data("dataPanelbeta")

Fitting Model

dataPanelbeta <- dataPanelbeta[1:25,] #for the example only use part of the dataset
area <- max(dataPanelbeta[,2])
period <- max(dataPanelbeta[,3])
result<-Panel.beta(ydi~xdi1+xdi2,area=area, period=period ,iter.mcmc = 10000,thin=5,burn.in = 1000,data=dataPanelbeta)
 #> Compiling model graph
 #> Resolving undeclared variables
 #> Allocating nodes
 #> Graph information:
 #> Observed stochastic nodes: 25
 #> Unobserved stochastic nodes: 42
 #> Total graph size: 339
 #> 
 #> Initializing model
 #> 
 #> Compiling model graph
 #> Resolving undeclared variables
 #> Allocating nodes
 #> Graph information:
 #> Observed stochastic nodes: 25
 #> Unobserved stochastic nodes: 42
 #> Total graph size: 339
 #> 
 #> Initializing model
 #> 
 #> Compiling model graph
 #> Resolving undeclared variables
 #> Allocating nodes
 #> Graph information:
 #> Observed stochastic nodes: 25
 #> Unobserved stochastic nodes: 42
 #> Total graph size: 339
 #> 
 #> Initializing model

Extract mean estimation

Estimation

result$Est
 #> MEAN SD 2.5% 25% 50% 75% 97.5%
 #> mu[1,1] 0.9713731 0.02328292 0.9079123 0.9625973 0.9777934 0.9868270 0.9960250
 #> mu[2,1] 0.9569757 0.03324846 0.8755690 0.9460993 0.9657183 0.9787156 0.9926591
 #> mu[3,1] 0.9393633 0.04957912 0.7970808 0.9236493 0.9520683 0.9707649 0.9901039
 #> mu[4,1] 0.9658961 0.02798058 0.8913413 0.9560956 0.9737534 0.9846068 0.9950255
 #> mu[5,1] 0.9385088 0.05338035 0.7846902 0.9230321 0.9543239 0.9729578 0.9901186
 #> mu[1,2] 0.9701842 0.02503484 0.9044870 0.9614728 0.9766194 0.9862512 0.9955072
 #> mu[2,2] 0.9652112 0.02802308 0.8904712 0.9554232 0.9725827 0.9833270 0.9942910
 #> mu[3,2] 0.9181959 0.06386394 0.7433878 0.8940435 0.9361087 0.9601812 0.9858488
 #> mu[4,2] 0.9763548 0.02105958 0.9189624 0.9700028 0.9827027 0.9903026 0.9969880
 #> mu[5,2] 0.9424182 0.04372767 0.8352181 0.9278862 0.9531731 0.9697931 0.9897842
 #> mu[1,3] 0.9687955 0.02724247 0.8923014 0.9611683 0.9762906 0.9867519 0.9958210
 #> mu[2,3] 0.8727048 0.08015318 0.6633978 0.8365484 0.8907476 0.9288464 0.9713757
 #> mu[3,3] 0.9589801 0.03034478 0.8803231 0.9463271 0.9666111 0.9799933 0.9936224
 #> mu[4,3] 0.9557647 0.03383615 0.8688497 0.9429073 0.9652019 0.9791047 0.9935937
 #> mu[5,3] 0.9257019 0.04910279 0.7971302 0.9066043 0.9372174 0.9590961 0.9849859
 #> mu[1,4] 0.9538652 0.03615603 0.8566988 0.9403275 0.9632428 0.9784399 0.9931700
 #> mu[2,4] 0.9392213 0.04329936 0.8217429 0.9241023 0.9499753 0.9683103 0.9885660
 #> mu[3,4] 0.9344597 0.04617361 0.8124747 0.9169184 0.9454070 0.9661673 0.9876194
 #> mu[4,4] 0.9724688 0.02626781 0.8988352 0.9651721 0.9801582 0.9885622 0.9965840
 #> mu[5,4] 0.8539960 0.10516566 0.5752763 0.8125300 0.8838448 0.9258455 0.9687237
 #> mu[1,5] 0.9656977 0.02847380 0.8953434 0.9565754 0.9734931 0.9845512 0.9953143
 #> mu[2,5] 0.8897345 0.07813767 0.6765461 0.8600749 0.9112217 0.9437139 0.9776705
 #> mu[3,5] 0.9598528 0.03131756 0.8717586 0.9484348 0.9682738 0.9808066 0.9937804
 #> mu[4,5] 0.9330710 0.04980811 0.7949374 0.9141878 0.9453854 0.9670004 0.9890399
 #> mu[5,5] 0.8682562 0.08506625 0.6421667 0.8302648 0.8900370 0.9289515 0.9685002

Coefficient Estimation

result$coefficient
 #> Mean SD 2.5% 25% 50% 75% 97.5%
 #> b[0] 2.005972 0.4063064 1.2091470 1.7307123 1.998160 2.277578 2.814624
 #> b[1] 1.112682 0.5038805 0.1361614 0.7630400 1.110898 1.461489 2.102108
 #> b[2] 1.120562 0.4591467 0.2195766 0.8216082 1.109322 1.440124 2.019678

Random effect variance estimation

result$refvar
 #> NULL

Extract MSE

MSE_HB<-result$Est$SD^2
 summary(MSE_HB)
 #> Min. 1st Qu. Median Mean 3rd Qu. Max. 
 #> 0.0004435 0.0007853 0.0013073 0.0024762 0.0024808 0.0110598

Extract RSE

RSE_HB<-sqrt(MSE_HB)/result$Est$MEAN*100
 summary(RSE_HB)
 #> Min. 1st Qu. Median Mean 3rd Qu. Max. 
 #> 2.157 2.903 3.790 4.858 5.338 12.315

You can compare with direct estimator

y_dir<-dataPanelbeta[,1]
y_HB<-result$Est$MEAN
y<-as.data.frame(cbind(y_dir,y_HB))
 summary(y)
 #> y_dir y_HB 
 #> Min. :0.3836 Min. :0.8540 
 #> 1st Qu.:0.9702 1st Qu.:0.9331 
 #> Median :1.0000 Median :0.9539 
 #> Mean :0.9423 Mean :0.9399 
 #> 3rd Qu.:1.0000 3rd Qu.:0.9657 
 #> Max. :1.0000 Max. :0.9764

MSE_dir<-dataPanelbeta[,4]
MSE<-as.data.frame(cbind(MSE_dir, MSE_HB))
 summary(MSE)
 #> MSE_dir MSE_HB 
 #> Min. :0.0004401 Min. :0.0004435 
 #> 1st Qu.:0.0036464 1st Qu.:0.0007853 
 #> Median :0.0228563 Median :0.0013073 
 #> Mean :0.0256965 Mean :0.0024762 
 #> 3rd Qu.:0.0428368 3rd Qu.:0.0024808 
 #> Max. :0.0887137 Max. :0.0110598

RSE_dir<-sqrt(MSE_dir)/y_dir*100
RSE<-as.data.frame(cbind(RSE_dir, RSE_HB))
 summary(RSE)
 #> RSE_dir RSE_HB 
 #> Min. : 2.098 Min. : 2.157 
 #> 1st Qu.: 6.039 1st Qu.: 2.903 
 #> Median :15.118 Median : 3.790 
 #> Mean :16.266 Mean : 4.858 
 #> 3rd Qu.:21.629 3rd Qu.: 5.338 
 #> Max. :59.741 Max. :12.315